Quadrilateral relationships answers
Note: you should make sure you understand the reasoning and examples,
not just the yes/no answer.
Squares:
1. Is every square a rhombus?
Yes, a rhombus is a quadrilateral with
4 equal sides. Every square has 4 equal length sides, so every
square is a rhombus.
2. Is every square a rectangle?
Yes. A rectangle is a
quadrilateral with 4 right angles. Every square has 4 right
angles, so every square is a rectangle.
3. Is every square a parallelogram?
Yes. A parallelogram is a
quadrilateral with 2 pairs of parallel sides. The opposite sides
on every square are parallel, so every square is a parallelogram.
4. Is every square a quadrilateral?
Yes. Every square is a closed
figure, and every square has 4 straight sides, so every square is a
quadrilateral.
Rectangles:
5. Is every rectangle a square?
No--Some rectangles are not squares.
This one is not, because it doesn't have 4 equal length sides:
No--Some rectangles are not rhombi.
This one is not, because it doesn't have 4 equal length sides:
7. is every rectangle a parallelogram?
Yes. A parallelogram is a
quadrilateral with 2 pairs of parallel sides. The
opposite sides on every rectangle are parallel, so every rectangle is a
parallelogram.
Yes. This shape has 4 right
angles, so it is a rectangle. It also has 4 equal sides, so it is
also a square.
9. Are there any rectangles that are rhombi?
Yes. This shape has 4 right
angles, so it is a rectangle. It also has 4 equal sides, so it is
also a rhombus.
10. Is every rhombus a square?
No. This rhombus
does not have right angles, so it isn't a square:
No. This rhombus
does not have right angles, so it isn't a rectangle:
12. Is every rhombus a parallelogram?
Yes. A parallelogram is a
quadrilateral with 2 pairs of parallel sides. The
opposite sides on every rhombus are parallel, so every rhombus is a
parallelogram.
Yes. This shape has 4 equal sides
so it is a rhombus. It also has 4 right angles, so it is also a
square:
Yes. This shape has 4 equal sides
so it is a rhombus. It also has 4 right angles, so it is also a
rectangle:
Yes. All of them are
16. Is every parallelogram a square?
No. This quadrilateral has 2
pairs of parallel sides, so it is a parallelogram, but it does not have
equal sides or right angles so it is not a square
17. Is every parallelogram a rectangle?
No. This quadrilateral has 2
pairs of parallel sides, so it is a
parallelogram, but it does not have right angles so it
is not a rectangle
No. This quadrilateral has 2
pairs of parallel sides, so it is a
parallelogram, but it does not have equal sides so it
is not a rhombus
19. Are any parallelograms squares?
Yes. This quadrilateral has
parallel opposite sides so it is a parallelogram. It also
has equal sides and right angles, so it is a square
20. Are any parallelograms rectangles?
Yes. This quadrilateral has
parallel opposite sides, so it is a parallelogram. It also has
right angles, so it is a rectangle
Yes. This quadrilateral has
parallel opposite sides, so it is a parallelogram. it also has
equal length sides, so it is a rhombus